Corresponding author: Olga N. Andrianova ( o.n.andrianova@yandex.ru ) Academic editor: Yury Kazansky
© 2021 Olga N. Andrianova, Yury Ye. Golovko, Gleb B. Lomakov, Yevgeniya S. Teplukhina, Gennady M. Zherdev.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Andrianova ON, Golovko YuYe, Lomakov GB, Teplukhina YeS, Zherdev GM (2021) Calculation and experimental analysis of benchmark experiments with a fast neutron spectrum and models of sodium and lead cooled fast reactors using different evaluated nuclear data libraries. Nuclear Energy and Technology 7(2): 103109. https://doi.org/10.3897/nucet.7.68951

The paper presents the results of a comparative analysis of criticality calculations using a MonteCarlo code with the BNAB93 and BNABRF neutron group constants, as well as with evaluated neutron data files from the Russian ROSFOND evaluated nuclear data library and other evaluated nuclear data libraries (ENDF, JEFF, JENDL) from different years. A set of integral experiments on BFS critical assemblies carried out in different years at the Institute of Physics and Power Engineering (60 different critical configurations) was analyzed. The considered integral experiments are included in the database of evaluated experimental neutronic data used to justify the neutronic performance of sodium and lead cooled fast reactors, to verify codes and nuclear data as well as to estimate uncertainties in neutronic parameters due to the nuclear data uncertainties. It has been shown that the ROSFOND evaluated nuclear data library is a library that minimizes the calculation and experimental discrepancies for the considered set of integral experiments. The paper also presents the results of criticality calculations for models of sodium and lead cooled fast reactors based on different evaluated neutron data libraries and provides estimates for the uncertainty in criticality associated with nuclear data.
Integral experiments, BFS facilities, ENDF, JEFF, JENDL, ROSFOND, BNAB93, BNABRF, sodium cooled fast reactor, lead cooled fast reactor
Refining the neutron data for the isotopes playing a crucial role in achieving the target level of accuracy when predicting analytically the neutronic performance of Generation IV reactors is an issue receiving a great deal of attention. The most prominent efforts were undertaken as part of the international project CIELO (Collaborative International Evaluated Library Organisation) (
ROSFOND, the commonly available official version of the national library of evaluated neutron data, (
One of the factors that hampers the introduction of updated neutron data library versions is the fear of discrepancies to be detected in the reactor performance calculations based on an updated library of neutron data and the predecessor library. At the same time, there is no surprise that such discrepancies can be observed, this being proved by analyzing the world experience in introducing updated versions of evaluated neutron data in the process of which the causes for potential inconsistencies are demonstrated and discussed.
The predictive capability and the efficiency of updated neutron data library versions are compared by matching the results of the performance calculations for critical assemblies with experimental data. In the paper, respective performance indicators were calculated and compared to identify highpriority activities on further enhancing the ROSFOND/BNABRF nuclear data libraries. It was used a representative set of experimental data measured on the BFS1 and BFS2 critical facilities. Respective calculations were performed using different versions of Russian (ROSFOND, BNABRF and BNAB93) and other evaluated nuclear data libraries (ENDF, JEFF and JENDL) from different years (ENDF/BV.2 (USA, 1994), ENDF/BVII.1 (USA, 2011) and ENDF/BVIII (USA, 2018), JEFF3.2 (Europe, 2014), JEFF3.3 (Europe, 2017) and JENDL4.0u2 (Japan, 2012)) (
Worldwide, the results of integral experiments are used for estimating and improving the accuracy of predictive calculations for reactor facilities and fuel cycle systems under design, planning new experiments, estimating the efficiency of experimental programs, etc. (
Table
Work has been initiated to form the databank for integral experiments based on BFS critical assemblies so that to systematize the accumulated information and enable its use for testing and adjusting evaluated nuclear data files, verifying codes, and estimating the accuracy of predicting the neutronic performance of fast reactors. This databank is designed to supplement the existing information and software tools to support the BFS experimental programs (
The criticality of the BFS critical assemblies shown in Table
Year  Assembly  Critical facility  Materials  Model 

Sodium cooled fast reactor  
1990  581 (1)*  BFS2  Pu/UO_{2}/Na/ inert diluter (UO_{2})  Sodium cooled fast reactors 
1993  661 (1)  Pu/UO_{2}/Na (UO_{2}/Na _{2})  
66B (9)  Pu/U(d)/C/Na/ (UO_{2}/Fe/Cr/Ni)  
1996  72 (2)  BFS1  U(d)/UO_{2}/Pu/Al_{2}O_{3}/Na (UO_{2})  
U(90/UO_{2}/ZrH/Na (UO_{2})  
1997  73 (1)  U/Na (UO_{2}/Na)  
1998  78 (1)  Pu/UO_{2}/Na (UO_{2}/Na _{2})  
Heavy liquid metal cooled fast reactor  
1991  611(3)  BFS1  Pu/U(d)/C/Pb/Al (Pb/UO_{2})  Lead cooled fast reactors 
1999  77 (2)  Pu/U(d)/UO_{2}/C/Pb (UO_{2})  
2000  641 (3)  BFS2  Pu/U(d)/C/Pb (PbBi)  
Hydrogencontaining materials (ICSBEP)  
2004–2005  97 (4)  BFS1  Pu/UO_{2} (UO_{2})  Fabrication of MOX fuel 
Pu/UO_{2}/CH_{2} (UO_{2})  
2008–2009  99 (3)  
101 (4)  
Nuclear waste disposal systems (ICSBEP)  
1999  79 (5)  BFS1  U/Si/CH_{2}  Waste disposal 
1999  81 (6)  Pu/Si/CH_{2}  
Different fuel compositions (ICSBEP)  
1974  31(2)  BFS2  Pu/UO_{2}  CNFC 
1976  33 (3)  UO_{2}/U(90)O_{2}  
1976  35 (3)  U(d)/U(36)/U(90)  
1977  38 (2)  Pu/U(d)  
1980  42 (1)  Pu/UO_{2}/CH_{2}  
1985  49 (2)  Pu/UO_{2}/CH_{2}  
Thermal reactors (IRPhEP)  
1989  57 (1)  BFS1  U(36)O_{2}/UO_{2}/CH_{2}/Al (UO_{2})  Thermal reactor models 
1990  59 (1)  Pu/UO_{2}/CH_{2}/Al (UO_{2}) 
Since the configurations of the critical assembly cores have a heterogeneous structure and represent alternating layers of different materials with a thickness of 0.3 to 100 mm, calculations in a group approximation need to take into account the heterogeneous resonant selfshielding of neutron crosssections. The calculations based on BNAB93 and BNABRF were performed using a subgroup representation of neutron crosssections in the resolved resonances region for the ^{238}U, ^{239}Pu and Fe isotopes and the neutron crosssection selfshielding factors for the rest of the isotopes and for ^{238}U, ^{239}Pu and Fe in the unresolved resonances region. The corrections for the selfshielding factors were calculated based on the principle of the equivalence of homogeneous and heterogeneous media. The procedures to calculate BFS critical assemblies using Monte Carlo codes in a group approximation are described in (
A statistical analysis was carried out using the calculation and experimental discrepancies for different versions of Russian and other evaluated nuclear data libraries, which makes it possible to conclude on the accuracy of calculations and the efficiency of describing a set of N integral experiments by the given system of constants L. Table
Neutron spectrum  Fast  Intermediate  All  

Indicator  ?  d  µ  ?  d  µ  ?  d  µ 
ROSFOND  –0.21  0.31  1.12  0.13  0.83  2.09  –0.10  0.54  1.53 
ENDF/BVII  –0.27  0.53  1.51  0.23  1.00  2.51  –0.09  0.72  1.92 
ENDF/BVIII  –0.22  0.40  1.31  0.37  0.88  2.70  –0.02  0.60  1.91 
ENDF/BV  –0.29  0.82  2.39  0.47  1.16  3.00  –0.03  0.94  2.61 
JEFF 3.2  –0.18  0.41  1.47  0.30  0.85  2.46  –0.01  0.59  1.87 
JEFF 3.3  –0.15  0.35  1.22  0.26  0.83  2.14  –0.02  0.55  1.76 
JENDL4.0  –0.02  0.47  1.11  0.46  0.87  2.34  0.15  0.63  1.64 
BNAB93  –0.09  0.63  1.98  0.30  1.12  2.87  0.05  0.83  2.33 
1. Average value of deviations of estimated multiplication factors from experimental values expressed as a percentage:
$<\Delta {>}^{L}=\frac{1}{N}\sum _{n=1}^{N}\left(\frac{{\mathrm{C}}_{n}^{L}}{{\mathrm{E}}_{n}}1\right)\xb7100$,
where ?_{n}^{L} is the calculated value obtained using library L for assembly n assigned to E_{n} (experimental value).
2. Rootmeansquare deviation of calculation and experimental relations for multiplication factors expressed as a percentage:
$<\delta {>}^{L}=\sqrt{\frac{1}{N1}\sum _{n=1}^{N}{\left({\Delta}_{n}^{L}<\Delta {>}^{L}\right)}^{2}}$,
where ?_{n}^{L} = (C_{n}^{L}/E_{n} – 1) is the calculation and experimental deviations in percentage terms obtained using library L for assembly n.
3. Number of standard deviations between the experiment and the criticality calculation, average for the set of N integral experiments, for the system of constants:
${\mu}^{L}=\sqrt{\frac{1}{N}\sum _{n=1}^{N}\left[{\left(\frac{{\mathrm{C}}_{n}{}^{L}{\mathrm{E}}_{n}}{{\mathrm{E}}_{n}}\xb7100\right)}^{2}\xb7\frac{1}{{\left({{\delta}_{\mathrm{E}n}}^{L}\right)}^{2}+{{\delta}_{\mathrm{C}n}}^{2}}\right]}$,
where d_{e} is the relative deviation of the experimental error, %; and d_{c} is the relative value of the calculated (statistical) error, % (
All values of the performance indicators in Table
Average deviations of calculated multiplication factors in transition from ROSFOND to other libraries
C^{i}/C^{ROSFOND} –1, %  

Average  Maximum  
BNABRF  0.11  0.34 
ENDF/BVII  0.23  0.86 
ENDF/BVIII  0.33  0.66 
ENDF/BV  0.66  2.35 
JEFF 3.2  0.26  0.70 
JEFF 3.3  0.24  0.84 
JENDL4.0  0.39  0.90 
BNAB93  0.44  1.66 
Table
$\Delta {C}_{\text{ROSFOND}}{}^{L}=\frac{1}{N}\sum _{n=1}^{N}\left\frac{{{C}_{n}}^{L}}{{{C}_{n}}^{ROSFOND}}1\right\xb7100$.
Fig.
Deviations in calculated criticality values caused by the transition from the evaluated nuclear data library’s older version to the new one: 1) magnitude (? ^{BNAB93}/? ^{BNABRF} –1) in percentage terms; 2) magnitude (? ^{ENDF/BV}/? ^{ENDF/BVIII} –1) in percentage terms. Regions shown by dashed lines: a) sodium cooled fast reactor; b) lead cooled fast reactor; c) fabrication of MOX fuel; d) waste disposal in sand; e) CNFC facilities.
Value of the deviation magnitude in calculations based on different libraries (?^{i}/?^{j} –1) in percentage terms: 1) minimum, 2) maximum. Regions shown by dashed lines: a) sodium cooled fast reactor; b) lead cooled fast reactor; c) fabrication of MOX fuel; d) waste disposal in sand; e) CNFC facilities.
Table
Deviations in k_{eff} calculations for fast reactor models involving the use of different evaluated neutron data libraries (C^{1}/C^{2}– 1, %)
Evaluated nuclear data library  Fast reactor 1 (Na+MOX)  Fast reactor 2 (Na+nitride fuel)  Fast reactor 3 (Pb+nitride fuel)  

C^{1}  C^{2}  C^{1}/C^{2}– 1, %  
BNAB93  BNABRF  0.09  0.52  0.89 
ENDF/BV  ENDF/BVIII  0.04  0.47  0.82 
ENDF/BVII  0.18  0.21  0.05  
ENDF/BVIII  0.07  0.03  0.05  
JEFF3.3  0.95  0.99  0.78  
JEFF3.2  JEFF3.3  0.23  0.24  0.03 
Based on covariance matrices and sensitivity coefficients of k_{eff} to the variation of the neutron crosssections, the k_{eff} uncertainty were calculated for fast reactor models which have been found to be 1.9% for sodium cooled fast reactors and 2.0% for lead cooled fast reactors.
Based on analyzing the results of the k_{eff} calculations for the entire set of the BFS critical assemblies, the following conclusions can be made.
Presentday Russian evaluated nuclear data and constants make it possible to calculate strongly heterogeneous BFS critical assemblies using precise Monte Carlo codes with high accuracy. The transition from ROSFOND to its group version, BNABRF, for the considered BFS critical assemblies leads to a deviation of the k_{eff} calculations equal to ~ 0.1% (see Table
The transition from BNAB93 to BNABRF leads to an increased accuracy of predicting k_{eff} for the BFS critical assemblies both with a fast neutron spectrum and with an intermediate neutron spectrum. On the average, the calculation and experimental discrepancies have decreased by a factor of one and a half to two; the criticality calculation values having changed by not more than 0.44% on the average. The maximum deviation of the k_{eff} calculations of up to 2% is observed for assemblies with an intermediate neutron spectrum and plutonium fuel. The maximum deviation value does not exceed the constant uncertainty for systems with an intermediate neutron spectrum, which varies in the limits of 2 to 3% depending on the assembly composition.
The transition from BNAB93 (1993) to BNABRF (2010) leads to deviations of the criticality calculation results for fast reactors with nitride fuel in the limits of 0.5 to 0.9%. The spread in the calculated k_{eff} values obtained based on stateoftheart U.S., European and Japanese evaluated nuclear data libraries from 2017–2018 is not less than ~ 1%.
The transition from JEFF3.3 and ENDF/BVIII of the 2010 and 2011 versions to the 2017 and 2018 versions did not lead to a more accurate description of the BFS critical assemblies and major deviations in the k_{eff} calculations for fast reactor models. However, when comparing the deviations in the BFS critical assembly k_{eff} calculations (see Fig.
The observed spread in the calculated k_{eff} values for the BFS critical assemblies and fast reactor models as a result of using different evaluated neutron data libraries does not exceed the uncertainty of the calculations caused by the neutron crosssection uncertainties.
The results of the calculation and experimental analysis presented in this paper for a set of experiments on BFS critical assemblies make it possible to conclude the following. The results of the k_{eff} calculations based on the ROSFOND evaluated nuclear data library may differ from the results obtained using certain versions of U.S., European and Japanese evaluated nuclear data libraries by about 1%. The differences between the calculated k_{eff} values obtained using JEFF 3.3 and ENDF/BVIII are also at a level of ~ 1%. When comparing different versions of the same library (e.g. ENDF/BV.2 (1994) and ENDF/BVIII (2018)) similar deviations are observed in the calculationexperiment results as in the event of the transition from BNAB93 (1993) to BNABRF (2010). It has been shown for the entire set of the considered experiments that the calculation and experimental discrepancies are smaller when updated versions of the evaluated neutron data libraries are used, as compared with the results obtained based on earlier versions of the respective evaluated nuclear data libraries.